This invention involves a modem which receives two or more streams or series of bits from respective data sources for transmission. The data bits to be transmitted are combined by multiplexing into a single stream and then arranged into groups of bits, each group defining a transmitted point or symbol. The size of each group depends on the type of modulation used. For example, if two 2,400 b/s streams of bits are combined into a single 4,800 b/s stream and 8-point QAM is used, then each group is formed of three bits. Next, each group of bits is translated into one of the QAM points and then transmitted. At the receiver the process described herein is reversed. During the separation of the bits the transmitter and receiver must by synchronized, otherwise the receiver would not be able to differentiate the bits which originated from different data sources.
Some problems have been encountered during the process of separating the bit stream. More particularly, it has been found that certain channel transmission line impairments cause synchronization between the receiver and transmitter to be lost. One solution to this problem has been proposed in U.S. Pat. No. 3,943,285. According to this patent, one group of signals is differentiated from the next by a 221/2.degree. phase shift. A disadvantage of this method is its susceptibility to error due to phase shift impairments.